Question: Simplify the following expression: $ q = \dfrac{-9}{8} + \dfrac{-r - 5}{5r} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5r}{5r}$ $ \dfrac{-9}{8} \times \dfrac{5r}{5r} = \dfrac{-45r}{40r} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{-r - 5}{5r} \times \dfrac{8}{8} = \dfrac{-8r - 40}{40r} $ Therefore $ q = \dfrac{-45r}{40r} + \dfrac{-8r - 40}{40r} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-45r - 8r - 40}{40r} $ $q = \dfrac{-53r - 40}{40r}$